Strange lights appearing
The blend file that you have provided doesn't render to the image above.  It is always a good idea to pack external files into the Blend file.  However, my guess would be the sun lamp you have in there is managing to reach that part of the scene and provide some highlights on the surfaces you are getting the bright spots on.  A quick test would be to turn off the sun and see if the bright spots remain.  If they go away then you can be sure that the sun is the source.  If you still want the bright area at the rear of the scene then you may need to rotate the sun a little or change it to a point source and add a Color/Light Falloff node into the strength.